\newproblem{lay:1_7_40}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 1.7.40}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
  Suppose an $m\times n$ matrix has $n$ pivot columns. Explain why for each $\mathbf{b}\in\mathbb{R}^m$ the equation $A\mathbf{x}=\mathbf{b}$ has at most one
	solution. [Hint: Explain why $A\mathbf{x}=\mathbf{b}$ cannot have infinitely many solutions.
}{
  % Solution
	In order to have infinite solutions, we need to have free variables that correspond to non-pivot columns of the matrix $A$. If $A$ has $n$ pivot columns, then there
	are no free variables, and there cannot be an infinite number of solutions.
}
\useproblem{lay:1_7_40}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
